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They say the problem is being caused by resource over-consumption on their web servers thanks to changes implemented over the past few days. Could those changes have anything to do with preparing a path for integration with Bing?
The status announcement says the changes were "necessary for the future growth of the product," which seems a bit of an odd moment of unnecessary justification. In any case, the tweaks caused some inefficiencies in the system that Twitter is now working to correct.